# Downlink Training in Cell-Free Massive MIMO: A Blessing in Disguise

## TL;DR

This paper demonstrates that downlink beamforming training in cell-free Massive MIMO systems significantly enhances achievable rates despite increased pilot overhead and contamination, especially when channel hardening is weak.

## Contribution

The study provides a closed-form expression for downlink rate considering channel estimation errors and pilot contamination, extending analysis to non-orthogonal pilots in cell-free Massive MIMO.

## Key findings

- Downlink training improves achievable rates despite increased pilot contamination.
- Channel hardening is less pronounced in cell-free Massive MIMO, making downlink training beneficial.
- Even with many APs, statistical CSI alone is insufficient for optimal data decoding.

## Abstract

Cell-free Massive MIMO (multiple-input multiple-output) refers to a distributed Massive MIMO system where all the access points (APs) cooperate to coherently serve all the user equipments (UEs), suppress inter-cell interference and mitigate the multiuser interference. Recent works demonstrated that, unlike co-located Massive MIMO, the \textit{channel hardening} is, in general, less pronounced in cell-free Massive MIMO, thus there is much to benefit from estimating the downlink channel. In this study, we investigate the gain introduced by the downlink beamforming training, extending the previously proposed analysis to non-orthogonal uplink and downlink pilots. Assuming single-antenna APs, conjugate beamforming and independent Rayleigh fading channel, we derive a closed-form expression for the per-user achievable downlink rate that addresses channel estimation errors and pilot contamination both at the AP and UE side. The performance evaluation includes max-min fairness power control, greedy pilot assignment methods, and a comparison between achievable rates obtained from different capacity-bounding techniques. Numerical results show that downlink beamforming training, although increases pilot overhead and introduces additional pilot contamination, improves significantly the achievable downlink rate. Even for large number of APs, it is not fully efficient for the UE relying on the statistical channel state information for data decoding.